## Properties of infinite groups::Local property

### ::concepts

Locally::space Group::property Locally::local Finite::small Circle::subgroup Finitely::spaces**Properties of infinite groups**
For an infinite group, a "small neighborhood" is taken to be a finitely generated subgroup. An infinite group is said to be **locally P** if every finitely generated subgroup is P. For instance, a group is locally finite if every finitely generated subgroup is finite. A group is locally soluble if every finitely generated subgroup is soluble.

**Local property sections**

Intro Properties of a single space Properties of a pair of spaces Properties of infinite groups Properties of finite groups Properties of commutative rings

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